no. 2
Spectral analysis in a thin domain with periodically oscillating characteristics
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 427-451.

The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). We consider all three cases.

DOI : 10.1051/cocv/2011100
Classification : 35P20, 49R05, 47A75, 35B27, 81Q10
Mots clés : spectral analysis, dimension reduction, periodic homogenization, Γ-convergence, asymptotic expansions 
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     author = {Ferreira, Rita and Mascarenhas, Lu{\'\i}sa M. and Piatnitski, Andrey},
     title = {Spectral analysis in a thin domain with periodically oscillating characteristics},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {427--451},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {2},
     year = {2012},
     doi = {10.1051/cocv/2011100},
     mrnumber = {2954633},
     zbl = {1248.35135},
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     url = {http://archive.numdam.org/articles/10.1051/cocv/2011100/}
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Ferreira, Rita; Mascarenhas, Luísa M.; Piatnitski, Andrey. Spectral analysis in a thin domain with periodically oscillating characteristics. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 427-451. doi : 10.1051/cocv/2011100. http://archive.numdam.org/articles/10.1051/cocv/2011100/

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